Why We Get Fat

Arthur De Vany

June 22, 2005

Contents

1 Introduction 3

2 Homeostatic Theories of Energy Management 4

2.1 Set Point Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 The Thrifty Gene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Body Composition 5

4 Fat as an energy adaptation 6

5 Starvation 7

6 Non-Linear Dynamics of Body Mass 8

6.1 Human Energy Expenditure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

6.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

7 Statistical Models of Energy Reserves 10

7.1 The Power Law Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7.2 The Gaussian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

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8 Positive Energy Balance as an Evolved Adaptation 12

9 Implications and Some Evidence 13

9.1 The Human Brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

9.2 Set Point Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

9.3 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

9.4 Body Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

9.5 Gene Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

9.6 Social Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

10 Conclusion 15

11 Appendix A 17

11.1 The Poisson Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

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1 Introduction

The simple answer to why we get fat may be that we eat too much. But, as Nesse and Williamswould say, that is only the proximate explanation; it may illuminate the underlying physiologicalmechanisms that result in obesity, but it does not explain why humans are inclined to eat in excessof energy expenditure. An evolutionary explanation requires that we discover the sources of thepossibly adaptive value of preferences and behaviors that are biased toward positive energy balanceto the human species. To do that I argue that we must move away from models of human feedingand energy management that are based on homeostasis.

The phrase “energy balance” subtly frames the issue of fat around the concept of homeostasis. Tosay that a person is fat because they overeat and so fail to maintain energy balance is somehowto say that energy balance is a natural or desirable state. A homeostatic theory of appetite andenergy management assumes that these systems are integrated in such a way as to maintain energybalance at some level. Is this theory true? What is the appropriate level of energy reserves?Are humans homeostatic energy managers? If they were, then homeostasis would be a naturalstate. But then how could anyone get fat? If homeostasis is natural, why is energy balanceso hard to achieve? It is far from clear that evolution would favor homeostatic mechanisms ofenergy control in the world of our ancestors. Such a mechanism is costly and may have had littlevalue in an ancestral world of scarce energy sources and high energy expenditure. A mechanismthat elicited feeding behavior only when energy resources were depleted and ensured no more thanrestoration of the depleted energy almost surely would result in starvation in the complex stochasticenergy environment of the Paleolithic. Modern obese humans demonstrate that evolved appetitemechanisms are capable of maintaining the body in a pathological state. Pathologically obeseindividuals do not experience diminished appetite in spite of their very large energy reserves. Howcould such an appetite mechanism evolve if it were part of a homeostatic system?

In this paper I want to argue and demonstrate that homeostatic theories of feeding and energyreserves are incorrect models of human (and mammalian) behavior. Homeostatic theories dominatea good deal of current thinking about obesity, particularly in the public mind and even (accordingto surveys) the thinking of health professionals. The “set point” theory of weight control, thatmakes so many so pessimistic about losing weight, is a well-known variant of homeostatic models.So is the “thrifty gene” model.

I argue that there is no adaptive value in maintaining energy balance in the world of our ancestorsand that human metabolism and feeding are not energetically balanced. Homeostasis in energyintake and expenditure and energy stores is not adapted to a complex energy environment. Humans,and other mammals, are “designed” to feed in excess of energy expenditure. Our evolved instinctsare to live in a state of positive energy balance in which we eat too much and exercise too little.This energy bias was adaptive in the world of our ancestors where high energy expenditure andfood procurement were intermittent and insecurely linked to one another.

I develop the argument by showing that human metabolism is non-linear and that body mass adaptsto energy intake and expenditure through a non-linear dynamic that converges to an attractor. Thisdynamic attractor exhibits some of the features that a “set point” theory tries to capture, but thereis no set point. Then I examine the complexity of the ancestral energy environment using models

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of stochastic energy expenditure and intake. I show through statistical and simulation modelsthat the best energy management strategy for ancestral humans was to “eat everything in sight”and to be as “lazy” as possible. Energy balance and homeostasis is a fatal strategy. These non-homeostatic models offer an explanation for the modern dilemma of obesity in humans living inWestern societies. We live in a non-complex energy environment of assured and abundant food andearn our living in sedentary jobs that, in effect, pay us not to exercise.

In the penultimate section, I discuss some of the implications of the models and the evidence. Then Iclose with some strategies suggested by the non-homeostatic model for achieving and maintaining ahealthful body composition more typical of the human species than the present generation exhibits.I find very strong results for energy expenditure relative to limiting energy intake. Relatively modestincreases in energy expenditure have more power to control body mass than much larger decreasesin energy intake. In other words, exercise is more powerful than dieting in bringing about a desirablebody composition. Some diets may lead to a dangerous loss of lean body mass, leading to organcollapse and/or heart damage and ventricular fibrillation.

2 Homeostatic Theories of Energy Management

2.1 Set Point Theory

The homeostatic theory of energy reserves dominates current thinking. The set point theory is ahomeostatic theory that proposes that declines in energy resources below their set point produceincreased feeding and energy intake until the set point is restored. The set point model dominatescurrent thinking about hunger and eating and weight control of lay persons and even health pro-fessionals. In this model, the body seeks to defend its energy stores through compensatory changesin appetite. To remain at a given weight, we must eat what we expend. If the set point theory isright, why is this so hard to do?

There is abundant evidence against the set point theory (see the reviews of Brandes, 1977; Friedman,Emmerich, and Gil, 1980; Smith, Gibbs, Strohmayer, and Stokes, 1972; Wilson and Davis, 1977;Woods, 1991). Obese individuals do not suffer diminished appetite. Paradoxically, they are oftenmore driven by hunger than people who are closer to a “normal” body weight. The set point theoryfails to account for the rise in obesity most people experience as they age. Are their set pointsdrifting up over time? Is the population of the United States undergoing an upward drift of theirset points as the incidence of obesity approaches 50%? What is the adaptive value of a set pointenergy management system that is capable of putting the body in a pathological state of obesity?

The set point theory is also incapable of explaining the wide range of energy reserves that we seeamong humans. Life can be maintained over a wide range of body weights and what is taken asnormal depends on the population. A modern, Western population has a range of body weights farlarger than any recorded for traditional hunter gatherers and this is true even when standardized forheight by such measures as BMI. Energy balance can occur at many different levels of body weight;a vastly over- or under-weight individual can be in energy balance at that weight, but it may beunhealthful. Health requires that energy balance be maintained at a desirable body composition.

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It is clear that hunter gatherers and likely our ancestors before them, maintained a different bodycomposition from modern humans; they had more lean body mass relative to fat mass. They alsowere more muscular and so carried more of their energy reserves in protein than in fat.

2.2 The Thrifty Gene

Another theory of energy reserves is the “thrifty gene” hypothesis. It proposes that evolution wouldhave favored individuals who were efficient in storing energy in a world where food was scarce andhigh energy expenditure was required to get it. Neel originally proposed the thrifty gene theory toexplain why some individuals get fat while others do not. But, in the United States, more thanhalf of us are fat and obesity is on the rise. To explain this pattern, most of us have to have thethrifty gene. That may be, but then what does the theory explain?

It is not clear at all that the ability to store energy as fat confers a selective advantage. To do thisrequires that the body divert the metabolic products of food from lean body mass to fat, sacrificingmobility, strength, and protein reserves. Thus, a thrifty genotype who stores more energy as fatwould be physically smaller than non-thrifty genotypes, with a smaller muscle and organ massrelative to body fat. What advantages could this altered body composition confer in survival andreproduction? How effective would a smaller ancestor with high body fat relative to lean bodymass be in the competition for resources and mates during the Paleolithic against larger and moremuscular, leaner individuals? I fail to see how a thrifty gene that favors the deposition of fat wouldconfer a selective advantage against non-thrifty genotypes. The evidence suggests that ancientas well as 20th century hunter gatherers carried more muscle and less fat than modern people.Moreover, the thrifty gene theory leaves open the question of homeostasis: does the thrifty geneset a high set point for energy reserves or does the gene enhance energy storage? In the first case,energy balance will be maintained at an altered body composition, in the second, energy balanceand body composition may drift. But, if energy balance drifts, then the theory fails to explainbody composition.

Clearly, with a thrifty gene or not, it must be possible for individuals to ingest more energy than theyexpend if they are to become obese. The “thrifty gene” hypothesis is an unsatisfying explanation(and may never have been offered for more than an explanation of why some get fat). We mustmake a distinction between an explanation of why an individual gets fat and another does not,versus an explanation of why all members of a species are vulnerable to obesity.1 Explaining whysome individuals get fat, say the Pima, and explaining why obesity is so common are separateproblems. It is the latter that I am addressing.

3 Body Composition

Fossil analysis indicates our species was derived from a tropical primate ancestor. Humans are notphysiologically adapted to severe cold. Even Eskimos are lean, on the order of 11% fat living the

1This paraphrases Nesse and Williams, p 17 where the discussion is about disease, but the distinction appliesequally well here.

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old ways. The Eskimo, as other humans do and have done for all time, use technology to cope withcold. Other animals do adapt their fat content to climate: whales carry up to 35% fat as insulationagainst cold, and the body fat composition of animals declines from the cold poles to the equator.

Cold-stressed humans, even those in populations known to have survived cold climates for millen-nia, survive through energy-consuming heat production rather than through the use of insulation.Metabolic heat produced through muscular activity, shivering or thermogenesis in brown fat com-pensates for heat loss to the environment. Even though humans are among the fattest of mammals,human response to cold stress does not rely on the build-up of fat. In fact, heat stress also in-creases the individuals energy needs. And human populations living in hot climates have as muchsubcutaneous fat as, or more than, the Eskimo.

4 Fat as an energy adaptation

If fat is not a cold adaptation then it is likely to be an energy adaptation; that both heat and coldincrease energy demands and makes the energy component of fat common to both. Thus, its role asan insulator is secondary to its role as a source of energy. Such reserves can be drawn upon duringtimes of food shortage and cold stress to support thermogenesis. Human fat depots are locatedat various sites around to body. Their distribution seems poorly designed for insulation and ismore likely a consequence of the ease of carrying fat as an energy store and as a shock absorberfor the organs. Fat reserves are mobilized by epinephrine which splits the triglycertriglyceridesidesinto free fatty acids and glycerol. The FFA are then split into acetyl-coenzyme A, which entersthe carboxylic acid cycle. During cold stress, lipoprotein lipase activity decreases in white adiposetissue and increases in brown adipose tissue. We were omnivorous from the beginning. Dentitionsuited to carnivory and plant eating exists in fossils over 2.5 million years old. Human ancestorshad the ability to exploit a range of foods, animal and vegetable matter. Dietary diversity permitsadaptation to changing climate and food sources. Dependance on a single source is risky. Storageof nutrient reserves (energy and vitamins and minerals) in fat is an essential element of thatadaptation.

The human brain has energy demands that are unlike those experienced by any other species. Thebrain consumes from one quarter to one third of the bodys basal energy demands. This is on theorder of 400-600 kcal/day. Since the brain relies on glucose, this translates into a demand for 100to 145 g of glucose/day. Coupled with this energy requirement is a high oxygen demand. The brainuses about 45% of the oxygen we breath and about two thirds of the body’s circulating glucose.These are demands which must be met or irreversible damage will occur. Contemporary brain sizeis from 1200 to 2000 g, the male brain being larger and requiring more calories. A progressiveincrease in brain size occurred during pre-hominid and hominid evolution. Australopithecus hada brain of 450-500 cc 2 million years ago; Homo erectus had a brain 1000-1100 ccs big 1.5-0.5million years ago. Coinciding with the growth in brain size, and energy requirements, is evidenceof increasing technological sophistication in tools whose purpose is directly related to hunting andthe use of animal sources of food. This is no coincidence, for the larger brains energy requirementscould only be met with nutritionally dense animal food. Tool making, large brains, and meat eatingcoevolved together.

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5 Starvation

Accompanying this coevolution of nutrition and large brains was the evolution of fat’s adaptivevalue as an energy store. A fat reserve gives one a longer term of survival during times of nutritionstress. But, weight loss during starvation (or a starvation kind of diet) is more than simply livingoff ones fat. There are energy and protein requirements to be met, as well as the need for essentialfatty acids. Vitamins, minerals and water are also requirements. To satisfy all these demandsduring food stress the body uses several lines of defense. First, energy demand is met by freeingglucose from liver glycogen. This lasts a few hours. Amino acids released from tissue then comeinto play. This is accompanied by a loss of minerals. To prevent electrolytic imbalance, there is ashedding of water, the main cause of weight loss during the first 5 days of a fast. Then fat lossesbegin. This too is non-linear. From the fifth to the ninth day of fast, about 4% of body weight islost most of which is fat. The rate of loss is about 500 g a day, but this drops to 100 g/day by the25th day of the fast. At this lower rate, a person can last a long time with no food.

But, not only is fat lost. Lean tissue and organ mass also are consumed. Even heart muscle issacrificed. A 20-year old girl who lost 128 lb. in 30 weeks consumed half her body’s lean tissuemass, including heart muscle. She died of ventricular fibrillation. The loss in lean tissue is requiredto supply the body’s continuing needs for amino acids. The muscle is a rich store of amino acids.When given up, these amino acids are not replaced unless the fast ends and protein is eaten. Thereleased amino acids are consumed in gluconeogenesis and in the synthesis of antibodies, essentialto the immune system. Exposure to infection increases the demand for amino acids to synthesizeantibodies.

As mammals, humans are continuous metabolizers and discontinuous feeders. This presents aninventory problem for energy reserves. Energy must be stored between meals and, given the rel-atively limited capacity for gluconeogenesis, mechanisms must be in place to preserve glucose forthe high energy human brain.

We may owe our large brains to our ability to get fat. Carnivores obtain long-chain fatty acids,essential to big brains, from other animals (Crawford and Marsh). Humans have large brains andsmall stomachs. We clearly are not herbivores, though plants occupy an essential part of the humandiet. Our metabolic rate is very high, because of our large brains, so high energy foods are essential,along with the long-chain fatty acids. We get them from animals, whose availability is seasonaland episodic. So, early humans embarked on a risky strategy for survival. We must therefore beable to store energy well, better than wild animals, who have only 4% body fat and better thanchimpanzees, the only primate other than humans that tends to get fat. Humans are, therefore, atthe high end of the scale in their ability to store fat.

A large-brained, small-stomached omnivore with long maturation time living on scarce, high valuenutrients and seasonal plant foods of varying quality faces a serious stochastic energy balanceproblem.

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6 Non-Linear Dynamics of Body Mass

In the following model, I discard the concept of homeostasis and argue that humans are far-from-equilibrium, open energy systems. The conditions of maintaining life are, therefore, different fromthose given by a linear, stable system.

6.1 Human Energy Expenditure

Farmers in Nepal expend from 1.89 to 2.01 times their basal metabolic rate (METS) in a day ofactivity. A worker spends about 1.7 METS. The Ache’ expend about 1.9. Office workers expendabout 1.3. Lumberjacks expend 6-8 METS. The highest sustained metabolic rates were recorded inthe Tour de France where, over a 22 day period, the cyclists maintained rates that were 4.3 timestheir basal rates. Mice, bees and other animals do not generally exceed 7 times basal metabolicrates on a sustained basis. All these field metabolic rates are well below the maximum that could beattained. Theoretical limit may be the inter-species limit of 1.7MJ/day/kg0.72. Competitors in theTour de France achieved over a 3 week period a daily energy expenditure of 1.6−1.8MJ/day/kg0.72.Higher rates seem to threaten survival and reproduction.

During the same period, the Tour de France competitors consumed an average of 24.5 MJ/day andexpended 29.4 MJ/day. They lost about 1.5 kg of lean body mass and about 2.3 kg of fat mass.Clearly, humans can expend energy well in excess of intake over a sustained period of time. Ofparticular interest is the adjustment of body mass to the sustained negative energy balance. Thisloss is not atypical of dieters, though dieters do tend to lose more lean body mass because they areless active than these competitive cyclers.

6.2 Model

Based on these considerations, I model body mass change in the following way. Let ∆w be thechange in body weight or mass in kg. Let ei be energy intake and let ee be energy expenditure. Tocomplete the notation for the variables in the model, let m be the metabolic rate as a proportionof the maximum sustainable rate of 1.6 − 1.8MJ/day/kg indicated in the data presented above.Estimates of the conversion of energy into body mass place the efficiency at 0.75. I include thethermic effect of food as a loss of ei0.1.

The equation for change in body mass then is

∆w = 0.75× (ei− ei0.1 −m× w0.72) (1)

In this model, energy balance is achieved when the change in body mass is zero. Body mass adjuststo a positive balance until body mass raises energy expenditure to equal intake. The responseto a negative energy balance is similar, though in this instance body mass declines until energyexpenditure matches intake. The solution for steady state body weight, given energy intake and

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expenditures of ei and m is the value w∗ such that ∆w = 0. Because ∆w is a concave and continuousfunction in w a solution will exist. The solution will depend on the parameters the human subjectsets; these are ei and m, representing energy intake and expenditure in multiples of the maximumsustainable metabolic rate.

For energy intakes of 5, 10, 15, 20 and 25 MJ/day and a metabolic rate of 0.5 of the maximalrate of 1.7MJ, the corresponding steady state body masses at which expenditure equals intake are16.87, 53.19, 99.17, 152.38, and 211.56. The caloric values of these intakes are from just over 1000to about 6,000 and the body weights, in pounds, range from about 35 to over 440.

On the expenditure side, for an intake of 12 MJ/day and metabolic rates of 0.2, 0.4, 0.6, 0.8, 1, thecorresponding steady state body masses are 252.05, 96.25, 54.80, 36.75, 26.95. Modest increases inenergy expenditure bring large reductions in body mass.

The dynamics of the process are very revealing. The solution for body mass now becomes a fixedpoint problem; starting at a mass of m0 the dynamics are a mapping to m1. We seek the solutionas a fixed point w∗ of the dynamic mapping M(wt) → wt+1; this is just the recursive dynamicwt+1 = wt + ∆w. Since the energetics are non-linear and concave, this will be a contractionmapping and a fixed point exists and is stable.

The gain segment of the mapping is shown in Figure 1. The loss segment is shown in Figure 2.It has a similar curved shape. The path to an equilibrium body weight has the distinctive curvetypical of weight gain and loss experienced by most people: an initially rapid gain or loss followedby a slowing and flattening. This path is suggestive of a set point in that the rate of gain or losseventually diminishes with further departures from the initial weight. But, what is really going onis that the path to the equilibrium weight to which the process converges is non-linear.

There is no set point, but there is a non-linear convergence to one of a multiplicity of equilibria, eachof which is individually consistent with a particular pair of values of energy intake and expenditure(ei, m).

Several propositions can be shown to follow from the model. The equilibrium is independentof initial body weight. The control parameters for each individual are ei and m; the remainingparameters are physiologically determined. Hence, a dieter who is undergoing acute weight loss willnot have reached equilibrium and may experience a transient reduction in metabolic rate becauseof diminished lean body mass along with the fat. Thus, energy expenditure will diminish even ifactivity is maintained at the rate set per unit of lean body mass. The energy deficit associated withthe initial conditions will diminish over the course of the decline in weight, and eventually reachzero, where the equilibrium weight will be established. Unless the subject continues to operate atthe same energy expenditure per unit of lean body mass and while maintaining the same energyintake, weight will not stabilize.

The weight regain that will be experienced if the subject returns to the energy imbalance that ledto the over weight condition will be rapid initially and non-linear also. Thus, an acute diet orexercise program that leads to a loss in weight will be followed by a rapid regain once the energydeficit is eliminated and a surplus corresponding to the original conditions is restored. Such anindividual, cycling through these acute stages, will seem to experience a return to a set point.

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Further implications of the model and the consistency with the evidence of these results will bediscussed later. Now we turn to the adaptive value of fat, that is to the evolutionary question:what is fat for?

7 Statistical Models of Energy Reserves

Humans are capable of expending levels of energy that exceed energy intake on a continuing basis.To do this, they rely on energy stores in muscle and liver glycogen, on gluconeogenesis of lean bodyprotein, and on fat. By far the largest reserve of energy is contained in body fat, though this clearlyvaries with the body composition of the individual. It has been estimated that even relatively leanindividuals carry enough body fat to support their basal metabolism for about 30 days. Less lean,but still not obese individuals may carry between 60 and 90 days worth of fat. Obese individualscarry enough fat to support their basal metabolism for one year. People living at a positive energybalance of as little as 3% will gain more than 40 pounds between the ages of 35 and 55, and this isroughly the pattern in the United States.

There is scant evidence to suggest ancient humans were obese and available evidence of naturallyliving hunter gatherers indicates they are uniformly lean, so we have a puzzle. My attempt to solveit is to look at the energy management problems humans may have faced in the roughly 3 millionyears that preceded the advent of agriculture.

I develop and examine stochastic models of energy expenditure and intake. I assume the form ofstatistical distributions of food encounters and energy expenditure and then examine the proba-bility of survival under different energy balance strategies. I examine models under three formsof statistical distributions. The first model assumes a Poisson distribution of prey encounters.Since the equilibrium of this model is death, it does little more than to illustrate the high stakesof the foraging life. I report the model briefly in Appendix A. The second assumes a power lawdistribution of energy expenditure and intake. The third is a variant of the second in which thedistributions are gaussian. All the models show that a positive energy balance strategy gives thehighest probability of reproduction and survival.

It would be more informative to follow the energy state of the forager and to use more realisticstatistical models. We turn to that task.

7.1 The Power Law Model

The energy environment of the Paleolithic was complex. There were intermittent periods of highenergy expenditure mixed with expenditures on many scales, with a high natural rate of expen-diture relative to Western living. A human forager would have frequent encounters of low energydensity plant food and less frequent encounters with high density animal sources. The possibilityof encountering extremely large prey would make the distribution of energy content of encountershighly skewed. A Rhinoceros or a Mammoth presents such a mass of energy that one or more suchencounters dramatically alters the average energy encounter rate. I assume that energy intake and

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expenditure follow power law distributions. I adopt a Pareto distribution as the model. A Paretodistribution is consistent with the energy expenditure data discussed above and would also appearto be a good approximation to the yields a forager would obtain. The possibility of extremely largeprey, such as a Rhinoceros or Mammoth, is well captured by the long tail of the Paretian distribu-tion which places more probability density on large events than would the Gaussian distribution.The same may be said on the expenditure side. The Paretian distribution, with its long tails, pro-vides a model of high frequency of low expenditures with rare, but large energy expenditures of thesort one would expect of a forager trekking long distances, hunting dangerous prey, and carryingheavy loads back to camp when the hunt is successful.

The Paretian energy intake distribution contains two parameters, a minimum and a tail weight.I choose these to reflect human energy metabolism. I set the minimum yield from foraging at0.5, which is scaled relative to basal metabolism. So, the value reflects that the minimum yieldfrom a day’s worth of foraging is about one half of basal energy expenditure. Corresponding tothe minimum energy intake, I set the minimum energy expenditure at 1.54, which reflects anexpenditure of 1.54 times the basal rate. This is the minimum for an active forager. The tailweight of the distribution of energy intake is set to equal 1.2. The tail weight of the expendituredistribution is set a 3.8. The parameters of the expenditure distribution are chosen to give a meanenergy expenditure consistent the evidence on hunter gathers. These parameters give a mean HGMET of 1.909, right about at what Leonard and Robertson estimate for the Ache’.

With these parameter values, the means for intake and expenditure are 3 and 2.09, reflecting akind of statistical abundance of food relative to energy expenditure. The variances of intake andexpenditure are ∞ and 0.6386. The infinite variance of the Pareto distribution for the tail weight1.2 simply reflects the high variance nature of energy expenditures of foraging. Infinite variance isnot surprising here, it simply means that the probability in the upper tail declines less rapidly thanx2 rises. This is perfectly consistent with the data gained monitoring the movements of wild fishand with estimates of the fractal dimension of the landscape over which our forager must travel.

A picture of the cumulative probability distributions is shown in Figure 3. With these distributions,the probability of energy intake less than expenditure is Pn = P [ei − ee < 0] = (1 − pdf(ei >h))(pdf(ee > h). The probability of negative energy balance can be obtained by numericallyintegrating this expression. The value quickly converges to 0.3437. The probability that depletionwould go on for a sufficient number of days to deplete reserves of R can be approximated by theprobability of a period of negative balances in succession sufficient to induce starvation. This isPS

n , where S = B/r is the number of days that would deplete an energy balance of B at the rateof r METS per day. Clearly, the chances of survival are greater the larger is B. To maximize thechances of survival, a forager in this environment must carry the maximal energy balance. Hence,it pays to have no upper bound on the energy the human body can store. Episodes of negativeenergy balance will be sufficient to maintain body fat in a physiological range, unless it becomesfully depleted and death ensues.

I have simulated the energy reserves under the conditions of the model to get some idea of thevariation that occurs and to gain some appreciation of the likelihood of death. These experimentsare shown in Figures 5, 6, 4.

The figures show that energy reserves are volatile, but they do not progressively become larger,

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even though the forager has been placed in an environment of abundant food. The reason isthat energy reserves are periodically drained through high expenditure, low intake, or both. Thelarge excursions through which energy balances move are pretty dramatic and indicate periods ofsubstantial withdrawals and gains.

What if the forager could take in no more than a portion of the food captured? Suppose theupper limit that could be consumed in a time period is three times the mean energy expenditure.That means that the forager could eat no more than three times average energy expenditure nomatter how large the take in a given episode. Such a limit makes survival more precarious, whichis evident from the calculation above and in the simulation of energy balance with an upper barrierin Figure 7

Energy balance is, on average, lower, makes smaller gains, and suffers losses that may substantiallyexceed the gains. Death by starvation becomes more probable. It seems unlikely that limitsstemming from energy balance considerations would have been adaptive in this environment. Theforagers best strategy, in the absence of food storage, is to eat to physiological limits wheneverpossible. If these limits can be extended by storing food, so much the better.

7.2 The Gaussian Model

The same kind of analysis can be done with gaussian distributions of energy intake and expenditure.The results strongly suggest that it is the high variance environment, not the mean energy intakeand expenditure that controlled body weight of pre-agricultural humans. When gaussian models areused with mean values close to those of the Paretian distributions, the results change dramatically.The gaussian distributions have less variance than the Paretian distributions, and the probabilitiesof large excursions in energy balance become small. The result is a diminished probability of deathby starvation and a much larger mean energy balance. This is true even with a much smaller biasof mean energy intake over mean expenditure than was true with the Paretian distributions.

Survival is still far from assured, though death has a diminished probability relative to the Paretianworld. The results show that our forager is fatter in a Gaussian world because energy reserves aredrained less often and the size of the drain is smaller each time one occurs. Most interesting isthe result that shows the forager gaining weight apparently without limit, something that did notoccur in the Paretian world. The low variance environment promotes weight gain with even asmall tendency to eat more than energy expenditure on those occasions when one does eat. Onecan suggest that the relatively assured supply of food and low variance energy expenditure aresignificant factors in modern obesity.

8 Positive Energy Balance as an Evolved Adaptation

The statistical models and simulations demonstrate the demanding energy management problemposed by the human adaptation. The solution is quite clear: eating to restore energy reserves isa fatal strategy—set point humans are dead. In their place are humans who posses the ability to

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eat well in excess of energy expenditures, and to do it on an extended basis. Such was a necessaryadaptation to uncertain energy expenditure and intake, which likely were distributed in a mannerthat spelled intermittent long spells of low intake and high expenditure. This is the prominentfeature of the power law or Paretian distribution of energy expenditure and encounter rates withgame. Enduring these spells required the ability to store energy in substantial amounts. Moreimportantly, it requires an uncoupling of appetite from energy expenditure. This means that inrelatively food replete conditions and sedentary activity levels, humans must have the appetite toconsume foods well in excess of energy expenditure. Given the intermittent, rare, but sometimesextreme episodes of large energy drains, an appetite mechanism that limited food intake duringtimes of energy surplus would not be sufficient to sustain the individual during these periods oflarge energy deficit.

The “risky” strategy of the human adaptation fundamentally altered the nutritional requirementsof humans, and especially of modern humans, relative to other animals. Humans were programmedto eat every thing in sight and lost the close feedback between energy expenditure and intake.They are programmed to balance energy over a longer time scale than other animals whose energyrequirements are lower, less intense, and whose food sources are readily available and not fugitive.

Insulin resistance is part of this adaptation. Insulin resistance spares scarce glucose for the brain.Following vigorous exercise, there is a transitory increase in insulin sensitivity and a decrease inthe utilization of protein that is used for gluconeogenesis. These changes serve to replenish muscleglycogen and to conserve on protein to make it available for muscle repair and rebuilding. Glucose isalso spared because GH lipolyzes adipose tissue so that free fatty acids serve as the energy substrateto support recovery. Fat is “there” precisely to support this regenerative process and to conserveglucose for the brain and for glycogen synthesis. For this to work, muscle has to be relatively moreinsulin sensitive than fat so that the energy available is redirected to brain and muscle tissue ratherthan into fat. There would have been a constant cycling of energy into and out of fat cells duringthe Paleolithic. This is something that does not occur among modern humans if they are physicallyinactive.

9 Implications and Some Evidence

9.1 The Human Brain

It is because we have big brains that we get fat. Insulin resistance is part of the equation for itconserves on glucose to preserve the brain, the essential instrument for our survival. In addition,a wide foraging range is required to exploit this strategy of fugitive high quality nutrients andomnivory. This adds an energy component of high activity per calorie and gram of protein gainedfor humans, which again is above that of many other animals.

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9.2 Set Point Theory

Obese persons generally regain lost weight, suggesting that adaptive metabolic changes favor returnto a preset weight. But experiments (Weinsier RL, Nagy TR, Hunter GR, Darnell BE, HensrudDD, Weiss HL, “Do adaptive changes in metabolic rate favor weight regain in weight-reducedindividuals? An examination of the set-point theory.” ) show that body composition adjustedRMR falls only during the acute phase of weight loss. Once body mass reached a steady state,adjusted RMR returned to the base state, before the weight loss. This is just as our model predictsand it shows that direct experiments reject the set point theory, which requires that adjusted RMRmust be lower in the new steady state in order to promote a regain to restore the set point. As themodel also shows, subjects who regain weight are those who fail to establish energy balance after theweight loss. They regain lost weight because they return to the energy intake and expenditure thatdetermined their steady-state weight they had before they began the weight loss program. This givesthe misleading impression that weight-reduced persons are energy conservative and predisposed toregain. What they are predisposed to are the habits that caused them to become overweight andwhen they return to them following a weight loss, they return to the weight consistent with thosehabits.

9.3 Exercise

It is not overeating, but under-activity that causes obesity. We are paid not to exercise now.

There is persuasive evidence that much obesity is due to under-exercising rather than overeating.In a series of randomized, controlled trials it was found that sedentary men who take up jogginglose body fat in proportion to miles run, increase their energy intake, and improve their lipoproteinpattern. In a 1-year comparison of fat loss by dieting vs. fat loss by exercise without dieting, bothmethods were found to be effective in moderately overweight men, and both approaches raisedplasma HDL cholesterol. It has also been demonstrated in overweight men and women losingweight on a prudent diet (low fat, low cholesterol) that adding exercise to energy restriction furtherincreased loss of body fat and reduced waist-to-hip girth ratio, especially in men. Risk of coronaryheart disease was also substantially further reduced by addition of exercise, in both sexes. Thesestudies suggest that regular exercise is a valuable addition to dietary change for weight control andreduction of risk of chronic disease in people of all ages.

The energy demands of physical activity must be sufficiently intense to trigger these changes. Fewmodern humans engage in activity vigorous enough to do this. And there must be enough muscletissue relative to fat tissue for the muscle to generate a sufficiently high energy demand to “drawdown” on fat reserves. If there is a high volume of fat relative to muscle tissue, then, even thoughmuscle is more insulin sensitive than fat, the fat volume will contain more receptors than the muscletissue. Consequently, energy will flow to fat on balance. The body composition of modern humansmakes it easier for them to “get fatter”. They have so much fat that their fat out competes theirmuscle (and organs) for energy. In addition, they are incapable of the vigorous activity that wouldmake inroads into their fat inventory.

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9.4 Body Composition

Modern humans have a body composition that is novel from the long perspective of the evolutionof the species. We have relatively more body fat relative to muscle than all of the hunter gathererpopulations that have been studied. Even the chubby looking Eskimo has only 10% body fat, solong as the subject lives in the traditional ways. Skeletal remains of pre-agricultural humans showrobust skeletons and strong attachment points on limbs that anchored powerful muscles.

Altered body composition is an adaptation to energy surplus. The dynamic model developed aboveonly treats total body mass, but it is clear that energy surplus increases fat mass relatively morethan lean muscle mass. The growth in body mass is the body’s attempt to achieve energy balance,even at what may be a dramatically elevated energy surplus.

9.5 Gene Expression

Genetic obesity begins at a young age, when gene expression is triggered by low energy flux, poornutrition, and excessive sugar and fat. This gene expression hypothesis may be the thrifty gene ormetabolic syndrome or some more complex process. We all (or most of us) have it to some degree,while the thrifty gene is hypothesized to be carried by only some of us.

The gene expression theory of obesity is different from the energy balance theory. It is a theoryof body composition. It goes something like: energy flow over metabolic pathways alters geneexpression and body composition. The flux on each pathway and the intermittent pattern turn ongene expression. So, you don’t have to have a “thrifty gene” to get fat, you can just turn on genesthat favor fat deposition through your activities and eating patterns.

By the time we are older, the pathways and gene expression already developed favor obesity. So,diets don’t work and this is well-established and powerful evidence.

9.6 Social Organization

A social organization that facilitated the sharing and storage of food would clearly have been auseful adaptation given the relatively poor prospects of survival of a forager in the conditions wehave modeled. Moreover, these innovations would have contributed to the evolution of a smallerstomach and release resources for metabolically expensive brain tissue. The evidence that socialorganization seems to have coevolved with larger brains is fully consistent with this.

10 Conclusion

Even obligate carnivores do not have the intense energy demands of the human brain and do notget fat; their body fat is on the order of 4%. Unlike wild animals and game, humans can and do

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greatly exceed 4% body fat. Our other big-brained relative, chimpanzees also are capable of pilingon excess fat and on average carry more body fat than other animals. A “natural” level of bodyfat is something like 11% among hunter gatherers.

I have shown that the “eat everything in sight” strategy is optimal for an ancestral forager. It alsois a good strategy to minimize energy expenditure relative to return. These pose a dilemma formodern humans; we seem designed to be “lazy overeaters”. Clearly, an uncoupling of intake andexpenditure is an essential adaptation. We have to be capable of overeating, even when sedentary,in order to overcome the large energy drains that would have characterized the uncertain energyenvironment of the Paleolithic hunter-gatherer.

Another point that comes through clearly in the models is that energy balance is something thatwould be achieved over relatively long time intervals for a foraging Paleolithic human. They wouldhave been in energy deficit as much as one third of the time and would experience some ratherpainfully long periods of hunger stress. But, given their intake and expenditure strategies, fewwould starve to death unless there were substantial shifts in the plant and prey distributions.

The modern idea that we should be in energy balance on an almost daily basis is not a natural con-dition and is dependent on a reliable supply of food. Almost surely, our ancestors spent intermittentand sometimes demanding episodes of energy deficit. The cycling of energy balance through burstsof expenditure and intervals of hunger is a powerful signal that alters gene expression. Caloricdeprivation studies seem to show chronic and acute energy deficit extends life and improves healthindicators such as insulin sensitivity. A related point is that increasing energy expenditure throughactivity or exercise is more powerful in attaining a healthy body composition and mass than isdecreasing energy intake. And extreme diets can be very dangerous.

We may owe our brains to our ability to get fat. Now, we just have to use them to overcome ourevolved instincts to live in a modern world of energy surplus.

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11 Appendix A

11.1 The Poisson Model

Assume that food encounters are discrete and follow a Poisson process. We will consider fourdiscrete energy states for the human forager who eats the food encountered in the following fashion.If no prey is encountered, the forager goes hungry and one unit of energy is drained from reserves.If one prey is encountered, the prey is eaten and energy taken in just covered the unit expended inforaging. If two prey are encountered, they both are eaten and energy balance goes up one unit.If more than two prey are encountered, only three are eaten and energy balance goes up to two.Thus, the energy states are 0, 1, 2, 3. From the Poisson assumption, we derive the transition matrixbetween states. The matrix of discrete transition probabilities is

m =

∣∣∣∣∣∣∣∣∣1 0 0 0

d(0) d(1) d(2) 1− (d(0) + d(1))0 0 d(1) d(2)0 0 d(0) d(1)

∣∣∣∣∣∣∣∣∣This simple model can be solved for the steady state probabilities of the states. Letting the vectorof steady state probabilities be ps, the solution satisfies m′ps = ps and p1 + p2 + p3 + p4 = 1. Thesteady state solution for any values of the parameters of the Poisson distribution is the probabilityvector for the states of (1, 0, 0, 0). That is to say, the probability of death by starvation is one inthe long run. The forager should eat everything she encounters. Preservation and storage wouldhelp as this would let the forager carry over encounters of prey larger than he can consume.

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Figure 1: Non-linear Loss

50 100 150 200

71.5

72

72.5

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74

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Figure 2: Non-linear Gain

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96

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99

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Figure 3: CDFs of energy expenditure and intake

2 4 6 8 10

-0.2

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1

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Figure 4: Energy Reserves: Run 1

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140

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Figure 5: Energy Reserves: Run 2

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Figure 6: Energy Reserves: Run 4

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Figure 7: Energy Reserves with an Upper Barrier

20 40 60 80 100

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35

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